Question

The following questions pertain to a harmonic oscillator. Express k-hat and v-hat in matrix form.

a. k-hat = [k, 0; 0, k], v-hat = [0, 1; -1, 0]
b. k-hat = [0, k; k, 0], v-hat = [1, 0; 0, -1]
c. k-hat = [k, 0; 0, -k], v-hat = [0, -1; 1, 0]
d. k-hat = [0, -k; -k, 0], v-hat = [-1, 0; 0, 1]

Answer 1

The correct answer is option a. k-hat = [k, 0; 0, k], v-hat = [0, 1; -1, 0].

Step-by-step explanation:

To express k-hat and v-hat in matrix form, we can use the given matrices for k-hat and v-hat and write them as follows:

k-hat = [k, 0; 0, k]

v-hat = [0, 1; -1, 0]

These matrices represent the coefficients for the x and y directions in a harmonic oscillator. The k-hat matrix represents the spring constant in the x and y directions, while the v-hat matrix represents the velocity in the x and y directions. These matrices can be used to solve problems in harmonic oscillators.